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Factor problem

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Factor problem

by gmat009 » Tue Oct 07, 2008 11:03 am
If n and t are positive integers, is n a factor of t?
(1) n = 3^(n-z)
(2) t = 3^n

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Edited my question....

OA is C but IMO E becoz nothing is mentioned about z, whether it is positive or negative which can change the answer
Last edited by gmat009 on Tue Oct 07, 2008 11:35 am, edited 1 time in total.
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by cubicle_bound_misfit » Tue Oct 07, 2008 11:15 am
IMO it is B.

if t = 3n
t has to have a factor as n.

experts please let me know where I am wrong.

regards,
Cubicle Bound Misfit
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by gmat009 » Tue Oct 07, 2008 11:35 am
cubicle_bound_misfit wrote:IMO it is B.

if t = 3n
t has to have a factor as n.

experts please let me know where I am wrong.

regards,
I am sorry, there was an error while posting the question. I corrected it.
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by gmat009 » Tue Oct 07, 2008 12:59 pm
Can someone help me in this........
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Re: Factor problem

by Ian Stewart » Tue Oct 07, 2008 3:13 pm
gmat009 wrote:If n and t are positive integers, is n a factor of t?
(1) n = 3^(n-z)
(2) t = 3^n

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Edited my question....

OA is C but IMO E becoz nothing is mentioned about z, whether it is positive or negative which can change the answer
Strange question- where did you find it? The answer is indeed E, at least as the question is presented. But I'm quite surprised nothing is mentioned about z. If you knew that z was an integer, the answer would be C.

Clearly neither statement is sufficient on its own. Taking them together: We know from statement 2 that t is equal to a power of 3, so we simply want to know whether n is equal to a smaller (or equal) power of 3. It certainly is if z is a positive integer, so together the statements are *almost* sufficient.

But we don't know anything about z, and in particular, z does not need to be an integer at all. So it's perfectly possible to have a situation like the following:

n = 2
z = whatever number z would need to be to make statement 1 true (z wouldn't be an integer, but that's fine)

Then t = 3^2 = 9, and n is not a divisor of t.

I'd note that the issue here is not whether z is positive or negative- z cannot be negative. From Statement 2 alone you can tell that n must be smaller than t, since 3^n will always be greater (and for large n, much, much greater) than n if n is a positive integer. If n is smaller than t, then 3^(n-z) must be smaller than 3^n, and z must be positive.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Re: Factor problem

by gmat009 » Tue Oct 07, 2008 3:25 pm
Ian Stewart wrote:
gmat009 wrote:If n and t are positive integers, is n a factor of t?
(1) n = 3^(n-z)
(2) t = 3^n

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Edited my question....

OA is C but IMO E becoz nothing is mentioned about z, whether it is positive or negative which can change the answer
Strange question- where did you find it? The answer is indeed E, at least as the question is presented. But I'm quite surprised nothing is mentioned about z. If you knew that z was an integer, the answer would be C.

Clearly neither statement is sufficient on its own. Taking them together: We know from statement 2 that t is equal to a power of 3, so we simply want to know whether n is equal to a smaller (or equal) power of 3. It certainly is if z is a positive integer, so together the statements are *almost* sufficient.

But we don't know anything about z, and in particular, z does not need to be an integer at all. So it's perfectly possible to have a situation like the following:

n = 2
z = whatever number z would need to be to make statement 1 true (z wouldn't be an integer, but that's fine)

Then t = 3^2 = 9, and n is not a divisor of t.

I'd note that the issue here is not whether z is positive or negative- z cannot be negative. From Statement 2 alone you can tell that n must be smaller than t, since 3^n will always be greater (and for large n, much, much greater) than n if n is a positive integer. If n is smaller than t, then 3^(n-z) must be smaller than 3^n, and z must be positive.
Thanks Ian for nice explanation..........
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